Problem: Determine the intercepts of the line. $y-4=7(x-6)$ $x$ -intercept: $\Big($
The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}{0}-4&=7(x-6)\\ -4&=7x-42\\ 38&=7x\\ \dfrac{38}{7}&=x\end{aligned}$ So the $x$ -intercept is $\left(\dfrac{38}{7},0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}y-4&=7({0}-6)\\ y-4&=-42\\ y&=-38\end{aligned}$ So the $y$ -intercept is $\left(0,-38\right)$. In conclusion, The $x$ -intercept is $\left(\dfrac{38}{7},0\right)$. The $y$ -intercept is $\left(0,-38\right)$.